论文标题
在超复杂网络上
On Hypercomplex Networks
论文作者
论文摘要
“复杂性”的概念在复杂的网络科学中起着核心作用。传统上，该术语被用来表达其复杂网络的节点度的异质性。但是，鉴于该度分布不足以提供给定网络的可逆表示，因此需要对其拓扑的其他补充测量来补充其表征。 In the present work, we aim at obtaining a new model of complex networks, called hypercomplex networks - HC, that are characterized by heterogeneity not only of the degree distribution, but also of a relatively complete set of complementary topological measurements including node degree, shortest path length, clustering coefficient, betweenness centrality, matching index, Laplacian eigenvalue and hierarchical node degree.提出的模型从统一的随机网络开始，即ERDOS-RENYI结构，然后应用优化，以增加网络整体复杂性的索引。已经考虑了一种优化方法。复杂性指数表达了几种考虑的测量值的分散。报道和讨论了几个有趣的结果，包括HC网络随着优化的进行，在测量的主要组成部分中定义了一个轨迹，倾向于偏离所考虑的理论模型（Erdos-Renyi，erdos-renyi，barabasi-albert，waxman，waxman，waxman，随机的几何图形图形和watts-strogatz），以前的案例（先前的案例）（先前的案例）。我们观察到，在大量优化步骤之后，外围分支往往会进一步增强这些网络的复杂性。
The concept of 'complexity' plays a central role in complex network science. Traditionally, this term has been taken to express heterogeneity of the node degrees of a therefore complex network. However, given that the degree distribution is not enough to provide an invertible representation of a given network, additional complementary measurements of its topology are required in order to complement its characterization. In the present work, we aim at obtaining a new model of complex networks, called hypercomplex networks - HC, that are characterized by heterogeneity not only of the degree distribution, but also of a relatively complete set of complementary topological measurements including node degree, shortest path length, clustering coefficient, betweenness centrality, matching index, Laplacian eigenvalue and hierarchical node degree. The proposed model starts with uniformly random networks, namely Erdos-Renyi structures, and then applies optimization so as to increase an index of the overall complexity of the networks. An optimization approach has been considered in terms of gradient descent. The complexity index expresses the dispersion of the several considered measurements. Several interesting results are reported and discussed, including the fact that the HC networks define, as the optimization proceeds, a trajectory in the principal component space of the measurements that tends to depart from the considered theoretical models (Erdos-Renyi, Barabasi-Albert, Waxman, Random Geometric Graph and Watts-Strogatz), heading to a previously empty space (low density of cases). We observed that, after a considerably large number of optimization steps, peripheral branching tends to appear that further enhances the complexity of these networks.
